If you don't make the challenge, nothing will happen, but you won't be able to start a new challenge until that one has ended. (I think you are only able to change your challenge starting date if you haven't had a qualifying flight within that period.) As for going for the challenge starting June 1, if you don't believe you can maintain your gold status for this year, then taking the challenge would guarantee your gold status through 2/07; on the other hand, a mileage run would help you pick up those last 4k points if you start on June 16, and you'd have platinum until 2/07 and gold through 2/08.
A few posters have claimed success with multiple platinum challenges, but there is no evidence that this is the rule and not the exception..